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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Matrix and Inverse Matrix Projective Synchronization of Chaotic and Hyperchaotic Systems with Uncertainties and External Disturbances

Discontinuity, Nonlinearity, and Complexity 12(4) (2023) 775--788 | DOI:10.5890/DNC.2023.12.005

Vijay K. Shukla$^{1}$, Prashant K. Mishra$^{2}$, Mayank Srivastava$^{3}$, Purushottam Singh$^{3}$, Kumar Vishal$^{4}$

$^{1}$ Department of Mathematics, Shiv Harsh Kisan P.G. College, Basti-272001, India

$^{2}$ Department of Mathematics, P.C. Vigyan Mahavidyalaya, Jai Prakash University, Chhapra-841301, India

$^{3}$ Department of Mathematics, P.G. College, Ghazipur-233001, India

$^{4}$ Department of Mathematics, Magadh University, Bodh-Gaya-824234, India

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Abstract

This paper investigates matrix and inverse matrix projective synchronization of chaotic and hyperchaotic systems with uncertainties and external disturbances. The sufficient conditions for achieving matrix projective synchronization (MPS) and inverse matrix projective synchronization (IMPS) of two chaotic and hyperchaotic systems are obtained. Two controllers, one for MPS and other for IMPS are designed for synchronization and based on the design, the synchronization of considered chaotic and hyperchaotic systems is achieved using these controllers. Lyapunov stability theory is used to study the problem and numerical simulations are introduced to exhibit the adequacy of the MPS and IMPS.

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